Mourinho worked with Ibrahimovic at Inter Milan and Manchester United but said signing the 38-year-old would not make sense with Harry Kane at his disposal.
“You are right about the connection, we have more than a connection,” Mourinho said when asked on Monday whether he would be trying to sign the Swede.
“I would say also passion and understanding, an amazing player and an amazing guy, but I would say ‘no’. No chance.
“We have the best striker in England, we have one of the top two or three strikers in the world, it doesn’t make any sense for a striker of Zlatan’s dimension, obviously in his late 30s, but still a striker that can play in any club in the world.”
It has been a hectic first week for Mourinho at the Spurs helm following his appointment last week.
After his unveiling to the media on Thursday, he had his first game 48 hours later at West Ham, which Spurs won 3-2, and is now preparing for a Champions League clash with Olympiakos on Tuesday.
Tottenham, who reached the Champions League final last season, would qualify for the knockout stages with a win or if they drew and Red Star failed to beat Bayern.
Mourinho said he had not yet contacted his friend Mauricio Pochettino, who was sacked by Spurs last week.
“I needed that little bit of space to process things when I left previous clubs,” said the former Chelsea and Manchester United boss. “It does not take just five or six days to be open again.
“You take a little bit of time to process things and understand and to think and rethink. You speak with people and in a couple of weeks he will be fine and I will call him.”
Part of Mourinho’s remit at Spurs is to do one thing that Pochettino could not do — win silverware.
“I love the competition (Champions League) as much as everyone in football,” said Mourinho, who won the trophy with Porto and Inter Milan.
“It’s something that everybody dreams about, to win it. Not everyone has the privilege to be a Champions League winner, which I was happy enough to do twice.
“Do I want to win it a third time? Of course, I would love it but I know the difficulties of it.
“But with these boys, I will never be afraid of any Champions League match that comes into our faces. I repeat, we need to qualify, that is the focus. I always say that.”
